Regional and interregional accounts in perspective

REGIONAL AND INTERREGIONAL ACCOUNTS IN PERSPECTIVE

By CHARLES I.. LEVEN, University of Pittsburgh

T H I S M A N U S C R I P T W I L L a t t empt to review crit ically the development of regional accounts, to comment on some misconceptions in the use of such accounts, and to make some suggestions for the direction of subsequent research. The discussion will be divided into four sections. First , there will be a discussion of the development of regional accounts up to this t ime. Second, some problem of measurement in implement ing the accounts will be reviewed and evaluated. The third section will consider some methodological issues, i.e., problems of formulat ing operational definitions and difficulties encountered in the analytical manipulat ion of the accounts. Finally, the fourth section will a t t empt a reconsideration of some of the conceptual issues in regional accounts analysis, wi th part icular reference to the theoretical notions about regional economic growth which underlie the accounts as they typical ly have been formulated.

Before proceeding to the substance of the discussion it might be well to define ra ther specifically what is meant by "accounts" and " regional . " "Social accounts" refers to the description of a part icular phenomenon as the sum of a set of components, where some of the components are free to vary, and the others will be assumed to bear a fixed relationship to the var iant ones. A sys tem of such accounts will be regarded as a description of those aspects of the region 's s t ructure that are involved with the phenomena which are being accounted for. Analytically, such a sys tem can be used to determine the effect on the s t ructure, as a whole and in detail, of changes in the independent variables within it. The changes in the independent variables will be regarded as having been generated out of some other analysis, or s t ipulated as policy al- ternat ive, at least in the case of those variables amenable to policy manipulation.

"Reg ion" will mean any continuous area which has ei ther an assignable spatial location or spatial ly definable boundaries, such that the functional relationships between the defined region and any other region depend upon their defined locations and/or boundaries. Metropoli tan areas or nonmetropol i tan "funct ional economic a reas" will be regarded as regions which typical ly have a high rat io of external to internal t rade and a high degree of economic inter- dependence among their inhabitants. 1

!. THE DEVELOPMENT OF REGIONAL ACCOUNTS

The description of the development of regional accounts contained in this section must necessari ly be brief, so there will be no a t t empt a t present ing a

1 "Functional economic areas" are multlcounty regions, generally centered around third-order central places, and have been suggested by Professor Karl A. Fox as logical spatial units for local economic development analysis and policy formation.

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complete bibliographical history, already available elsewhere. 2 Also, no at tempt will be made to trace the developments in economic base analysis prior to the series of articles by Richard B. Andrews appearing in Land Economics about ten years agoJ There are two reasons for this; first, such developments have been traced rather thoroughly by Professor Andrews in that series, and second, prior to that time the interests of economists in regional analysis were quite limited and there were not any regional scientists, or at most one, to be interested.

Also, the discussion will omit any consideration of the much longer tradi- tion in the estimation of aggregate or per capita income payments for small regions like counties. 4 While related to work in regional accounts, such estimates are not directly aimed at the analysis of regional economic structure, but at interregional comparisons of real income and sometimes the distribution of income among major classes of factors of production. Similarly, there will be no direct a t tempt to cover developments in what could be called the analysis of interregional convergence, usually directed at the testing of convergence hypotheses with respect to levels of real per capita income, wage rates, or rates of return of capital. ~ Finally, there will be no explicit consideration of intrametropolitan transportation and land-use models. 6 At least up to this point, most of the work on such models does not really fit the preceding definition of accounts, but rather is more closely related to distributional solutions of sets of spatial equilibrium equat ions/

Turning then to the Andrews articles as a start ing point, it seems reason- able to inquire as to why they can be so regarded. An obvious point is that they were contemporaneous with the really serious beginnings of regional science as a discipline; but so was a good deal of other work on the economic base by

2 See especially W. Isard, Methods of Regional Analysis, ch. 5 and Harvey S. Perloff, Regional Studies at U.S. Universities, (Washington, D. C., Resources for the Future, Inc., 1957).

8 R.B. Andrews, "Mechanics of the Urban Economic Base" a collection of reprints of articles in Land Economics, XXIX-XXXI, 29-31 (May, 1953-February, 1956).

Lewis C. Copeland, Methods for Estimating Income Payments in Counties (Univer- sity of Virginia, Bureau of Population and Economic Research, 1952) contains descriptions of techniques and an excellent bibliography of work up to that period. Since then there have been few methodological developments, but several in regard to data retrieval.

5 For examples and discussion of "convergence" studies see R. Easterlin, "Interregional Differences in Per Capita Income, Population and Total Income, 1840-1950)' National Bureau of Economic Research, Studies in Income and Wealth, XXIV, and G. Borts and J. Stein, "Investment Return as a Measure of Comparative Regional Economic Advantage," in W. Hochwald, ed., Design of Regional Accounts, (Baltimore, Johns Hopkins University Press, 1961).

6 Note the prominence given to these articles in John Meyer, "Regional Economics: A Survey," The American Eoonomic Review, March, 1963.

J. Herbert and B. Stevens, "A Model for the Distribution of Residential Activity in Urban Areas," Journal of Regional Science, Fall, 1960, and B. Harris, "Linear Pro- gramming and the Projection of Land Use," Penn-Jersey Paper No. 20, Penn-Jersey Trans- portation Study, 1963.

LEVI;N: REGIONAL AND INTERREGIONAL ACCOUNTS IN PERSPECTIVE ] 2 9

geographers and planners. But the interest ing thing about the Andrews articles is that they are f requent ly quoted in the l i terature of regional science and regional economics. And this continues to be the case in spite of the fact tha t besides a very complete review of fair ly obscure earlier work (which itself is hardly ever cited) the series contains very little, if any, of what could current ly be regarded as useful technique, and no theoretical discussion beyond very e lementary economic base ideas. 8

Actually, the real significance of the Andrews work is t h a t ' i t represents the first a t t empt to look at economic base studies, not as a mechanical analytical device, but as embodying a conceptual notion wor thy of critical evaluation. In most earlier work the economic base was an expedient technique for es t imat ing the future population of a city. I t was developed pr imar i ly in conjunction with studies done by the Federal Housing Adminis t ra t ion during the thirties. The i r problem was a simple one; at least s imple to state. In making plans for public housing, they were concerned with the future demand for housing. The notion of the economic base, essentially borrowed f rom the New York Regional Study of 1928, 9 reduced the problem of es t imat ing total fu ture population to es t imat ing fu ture " town-bui ld ing" employment , with an assfimed fixed rat io of "town-fi l l ing" to " town-bui ld ing" employment and a fixed number of inhabi tants per employed worker. True , the economic base idea did rest on certain conceptions of a s t ructural nature, but only in a ra ther vague way.

In Andrews ' articles, however, the economic base for a lmost the first t ime is regarded pr imar i ly as a vehicle for describing and analyzing a region 's economic s t ructure , 1~ and the process of regional growth itself. Quite natural ly, he considered, among other things, the unit of measurement of the economic base. As long as the base idea was nothing more than a technique for est imat- ing employment this question was meaningless. In a theory descript ive of the process of regional change, however, the question of "Change in Wha t? " became significant. Andrews considered a var ie ty of a l ternat ives (employment, payrolls, sales, value added, etc.) and came up with the idea that one should use all of these measures simultaneously.

The present author on first looking into Andrews was not convinced. In accordance with good Keynesian theory, it seemed that the lack of precision in Andrews ' research recommendat ions was unnecessary. Income, employment and production were all functionally related and so a plea was made for "va lue added" as the appropr ia te measure; not as conventionally defined, however,

8 Interestingly, the item of earlier work which probably most nearly anticipated current work in regional accounts, "Oskaloosa vs. the World," Jao~ucze, April, 1938, is not even referred to in the Andrews work. Another example of earlier work anticipating later developments is various unpublished manuscripts of Professor David Crane, Department of City Planning at the University of Pennsylvania, in connection with a study of Massachusetts communities which was done in the late forties.

9 Andrews, op. cit., for a description of this study. 10 Although not in economic base terms, the Fo~une article cited earlier would have

to be regarded as an exposition of regional economic structure.

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but as value added at all stages of production in the region, commodity by commodity--sor t of a gross product by industrial origin, it

Another appeal of the value-added or gross-product concept to those with a background in economics was that it lent itself readily to the making of allowances for charges against a region's trade balance as well as for credits to it. After all, if the planners and geographers felt that it was export trade that determined a region's future, the least the economists could do was to give them a comprehensive measure of it. This led to the notion of an extended rest of the world account as central to the analysis, and this led, rather naturally, to the formulation of a set of double-entry income and product accounts for a regional economy. 1~

To a considerable extent these accounts and regional accounts that have been formulated since that time are step-children of the United States national income accounts. The handling of government requires somewhat special consideration since, for a region, the federal government occupies a super-regional position. The rest of the world account generally has received a more complete statement than in the national accounts; in particular, flows of factor payments over the borders are treated explicitly, instead of being suppressed into the current commodity flow figures as is done for the United States. Exports are regarded as including "invisibles," as in the case of the United States accounts, but unlike the t reatment in conventional economic base studies.

Probably the most important innovation is the addition of indirect to direct exports, that is the value added in the production of raw materials for export. This innovation was necessary to get to a measure of gross product, rather than income, by industrial origin. The gross-product concept appeared necessary to account for differences in the commodity composition of changes in export demand, and their effect on the final equilibrium level of gross regional product. ~8 Finally, Professor Tiebout demonstrated the similarities between the economic base concept, and the more familiar concept of the foreign-trade multiplier. 1~ The regional economists felt quite comfortable.

Contemporaneous with the developments discussed above, a number of specific empirical regional interindustry studies were made. 15 These, too, were

11 C.L. Leven, "An Appropriate Unit for Measuring the Urban Economic Base," Land Economics, November, 1954.

~* The first explicit formulation of income and product accounts for a region occurred as part of the background analysis for a series of community studies appearing in the 1954 Annual Report of the Federal Reserve Bank of Chicago. Their formulation was jointly conceived, though perhaps not for the first time, by the present author and Professor Dick Netzer, both then members of the bank's research staff.

13 Leven, "Regional Income and Product Accounts: Construction and Applications," in W. Hochwald, ed., Design of Regional Accounts, (Baltimore, Johns Hopkins University Press, 1961) for further discussion of the treatment of indirect exports.

~* C.M. Tiebout, "Regional and Interregional Input-Output Models: An Appraisal," The Southern Economic Journal, October, 1957.

25 As examples see W. Hirsch, "Application of Area Input-Output Analysis," Regional Science Association Papers and Proceedings, V (1959); W. Isard and R. Kuenne, "The Impact of Steel upon the Greater New York-Philadelphia Industrial Region, The Review of Economics and Statistics, XXXV, November, 1953; F. Moore and J. Peterson, "Regional Analysis: An Interindustry Model of Utah," The Review of Economics and Statistics, November, 1955; and W. Hochwald, H. Striner, and S. Sonenblum, Local Impact of Foreign Trade, (Washington, D.C., National Planning Association, 1960).

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cast substantially in the image of their ancestors at the national level, usually with even less alteration of their format than in the case of regional income accounts. 1~ Regional input-output models will be discussed in another paper at these meetings, but one point only might be noted here, namely that it took several years for it to become clear that these two kinds of analyses were much more complementary than competitive. 17 The derivation of figures for indirect exports in the accounts does require an interindustry calculation, and the input-output analyses would seem to require some kind of multiplier analysis to estimate final demand in the household sector.

Another development in regional accounting which deserves at least some mention is a number of brief forays into accounting for moneyflows on a regional basis, is A major factor underlying these studies is the unsuitability of a conventional savings and investment account, in real terms, as a tool for analyzing the warranted rate of growth of a region. The net foreign investment residual in the income and product accounts simply does not have much significance for an "open" region where capital movements are not only large, relative to real capital formation, but also frequently contractual on a fairly long-term basis. The moneyflows accounts at tempt to trace out some or all of these gross capital flows, but in retrospect it does not seem that the question to which they are directed is a particularly interesting one. Potentially, they might be useful for explaining regional differences in the cost of capital, or other prices for that matter, but this has not been gone into at all thoroughly. 19

There are a few other developments which should be noted. Accounts have been formulated directly in terms of employment, 2~ and suggestions for formulat ing them in terms of land use have been made. 21

In some accounts studies, the sectors of final demand have been broken down, but only as subcategories of the basic four-section division in the national income accounts. 22 Finally, suggestions have been made for broadening the scope of phenomena covered, particularly with respect to the social costs and benefits of local government activities 23 and to the inclusion of an accounting

~s And in some cases, they assumed that the regional coefficients were equal to those for the United States.

i~ Leven, op. cir., for a discussion of this point. ~s Penelope Hartland, Balance o f Interregional Payments of New England, (Provi-

dence, Brown University Studies, XIV, 1950) and G. Hile, "The Balance of Payments of the Southeast in 1950," Regional Science Association Papers and Proceedings, I (1955).

19 C. Leven and H. Perloff, "Towards An Integrated System of Regional Accounts; Stocks, Flows and the Analysis of the Public Sector," in W. Hirsch, ed., Studies in Regional Accounts, (Baltimore, Johns Hopkins University Press, 1964) footnote 8, for a suggestion on this point that was made by Professor Ruth Mack.

2o C.M. Tiebout, Mac'kets for California Products, (Sacramento, California Develop- ment Agency, 1962) and E. Hoover, et al., Region with a Future, (Pittsburgh, University ,of Pittsburgh Press, 1964).

~1 Leven, op. cir. 32 Tiebout, op. cir. 2~ Hirsch, "A General Structure for Regional Economic Analysis," in W. Hochwald,

vp. cir.

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for stocks of human and nonhuman resources associated with the conventionally accounted for activity flows. ~4

While considerable interest has been expressed in interregional accounts, the only ones actually implemented empirically have followed a fairly straight- forward input-output framework. 3~ So far as regional income and product accounts are concerned, no real at tempt at implementation has been made, although the definitional comparability between accounts as formulated for a single region and Lloyd Metzler 's concept of interregional multipliers has been pointed out. 26

The foregoing discussion is intended to describe more or less where we are now with respect to the design and scope of regional accounts systems. The remainder of this paper will be concerned with a critical evaluation of some problems of measurement, methodology, and theoretical concepts. No at tempt will be made, however, at a chronology of such developments, but rather, the discussion will be limited to those issues which seem at present to be still unresolved, together with some suggestions for future research directions which might aid in their resolution.

IL SOME PROBLEMS OF MEASUREMENT

This section will not at tempt to assess either the emergence of or resolution of data limitations per se. Unavailability and unreliability of data needed to implement empirically regional accounts certainly have been and continue to be serious research problems. Most of these problems relate to the lack of coordination and sometimes lack of competence of many state and local statistical agencies and to limited access dictated by rules against disclosure. 37 These kinds of problems, however, extend to all phase of regional analysis and regional science and are not peculiar to regional accounts. Here the discussion will be confined to problems of measurement in principle.

One issue of interest is the question of the extent to which estimates of particular regional parameters can be obtained by disaggregation of national data. In part, this is simply a matter of disclosure, but there are also more basic matters. Most important, there is no way to derive the detailed information on interregional commodity flows (except for I. C. C. waybill data which is of only limited usefulness), labor commutation and capital transfers from present

34 H. Perloff, "Relative Regional Economic Growth: An Approach to Regional Accounts," in W. Hochwald, oi9. cir., and C. Leven and H. Perloff, op. cir.

35 For example, L. Moses, "The Stability of Interregional Trading Patterns and Input- Output Analysis," The American Economic Review, December, 1955.

28 Leven, op. eiL, and L. Metzler, "A Multiple Region Theory of Income and Trade," Econometvlca, October, 1950.

37 It should be noted that disclosure problems are becoming less serious. The Bureau of the Census will process individual respondent data for nongovernment researchers where the results, but not the individual respondent data, are sufficient. What still is needed is a way of confidentially processing individual respondent data from the census with individual respondent data from a variety of other sources without disclosure to the researcher or the respective statistical agencies. This is a useful function which might be solved through the establishment of regional data centers.

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national data sources, as all of these movements sum to zero for the nation as a whole, as The possibilities for developing regional measures of input coefficients for individual industries (which might be useful in some contexts, as will be pointed out later) also appear doubtful, at least so far as the author under- stands the United States Department of Commerce's data collection procedure. It does seem possible to obtain some regional measures of the pattern of consumer spending from survey work done in connection with the Consumer Price Index. Nevertheless, the prospects of deriving regional accounts data primarily from existing federal data collection programs do not appear bright. 2~

A more specific measurement problem which has received considerable discussion is that of determining an efficient and accurate means for estimating the export flows from a region, by commodity, The technique of "localization coefficients," frequently used in traditional economic base studies was discarded by regional scientists at an early stage. In addition to its inherent assumptions of interregional homogeneity with respect to production functions, consumption patterns, and even product mix, it also measures only "ne t " as opposed to "gross" exports; it is the latter which are relevant for multiplier calculations. 3~ Thus, by underestimating exports, it overestimates the size of the foreign-trade multiplier. And even worse, this technique will produce a consistently more downward biased estimate of exports, the greater the degree of aggregation employed in classifying industries. 2~

Thus, except for one possibility, there would seem to be a general con- sensus that direct commodity flow information is necessary to determine export flows. The possible exception is the "minimum requirements" technique, which estimates exports as the excess of regional production over the amount indicated by a regression relationship between regional population and the minimum per cent of the labor force employed in each of several regional-size classes, in any particular commodity classification. 22 Unpublished calculations, using the minimum requirements technique, which were made by Professor Ullman for Sioux City, show considerable variations from survey-determined data for individual broad industry groupings, but produce a total export estimate prac- tically identical to that determined from the surveys. 32 This suggests the

38 That such information could be collected by a federal agency is, of course, true, but this would represent a new data gathering task.

29 For further comment on this point see R. Ruggles and N. Ruggles, "Regional Break- downs of National Economic Accounts" in Hochwald, op. eit.

s0 For a fuller discussion of these limitations see H. Blumenfeld, "The Economic Base of the Metropolis," Journal of the American Institute of Planners, Fall, 1955, and C.L. Leven, Theory and Method of Income and Product Accounts for Metropolitan Areas (Pittsburgh, Center for Regional Economic Studies, University of Pittsburgh, 1963, reprint).

81 C.L. Leven, "A Theory of Regional Social Accounting," Regional Science Association Papers and Proceedings, 1958, for further discussion of this point.

82 E. Ullman and M. Dacey, "The Minimum Requirements Approach to the Urban Economic Base," Regional Science Association Papers and Proceedings, 1960.

a~ The published data based on field survey can be found in Sioux City Planning and Zoning Commission, "Economic Report, 1959."

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possibility that the minimum requirements technique at least is unbiased and perhaps even better. I t would seem useful to engage in some further testing of this hypothesis, particularly in light of the very much lower cost of making these kinds of calculations as opposed to pr imary data collection. Moreover, even if not generally applicable, they might be fairly reliable estimators for selected commodity classes.

Another measurement problem has concerned the allocation of undistributed corporate profits of multiregional firms. Taking the expedient of assuming that they should he accounted for as accruing all to home offices, 84 there remains the problem of estimating the excess of profits earned in "foreign" branches of "domest ic" corporations over those earned by "domest ic" branches of " fore ign" ones. In an income accounting system such an estimate is necessary as a component of the term ( F ~ - F~) in the relationship

Y . = Y ~ - ( F ~ - F ~ ) - ( T ~ - - T ~ ) - - ( U ~ - - U~o) - W ~ - - B ~

where YR is income of the region's residents; Ye is net product in the area; 35 F, , and F~, are factor payments, T~ and T,~ are taxes and government transfer payments, and U,~ and U~ are unilateral transfers received from and paid to abroad, respectively; W, is undistributed profits of domestic corporations; and B~ is business transfer payments from domestic firms to the region's residents. 86 In any accounting system, though, as many items as there are linearly independent relationships in the system can be determined as residuals. Thus, if any of the items so determined in the system containing this relationship can, alternatively, be estimated directly, then the net inflow of undistributed corporate profits component of ( F ~ - F~) can be determined as a residual. Personal income accruing to the region's residents, YR, would seem to be such an item. Moreover, the prospects for obtaining estimates of this item from Bureau of Internal Revenue statistics seem quite good, at least in principle. And, even in the absence of this possibility, estimating county or multicounty regional personal income by applying allocation techniques to state income payments data probably should have appeared more appealing than t rying to estimate interregional corporate profits flows all along. This also indicates that the whole discussion of the appropriate regional allocation of such undistributed profits was rather pointless; their only purpose was to get to an estimate of Y~. Interestingly, though, what appeared to be an arbitrary expedient, assign- ing them to home offices, now appears to be logically consistent with the remainder of the system. 87

8t For a justification, see Leven, Ioe. cir., pp. 53-55. s5 In earlier statements, this term was ambiguously defined simply as "income produced

in the region," with no allowance for subtraction of capital consumption allowances of domestic establishments.

86 For a complete description of the specific system of which this relationship is a part, see Leven, "Regional Income and Product Accounts, Construction and Application," in Hochwald, op. cir.

37 The author is indebted to Sigmund Wolkomir, a student in his course in regional analysis, for suggesting the points raised in this paragraph.

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The final measurement problem which will be discussed concerns the appropriate s t ra tegy for obtaining the data on inter industry flows needed to determine the amount of production ac t iv i ty going indirectly into expor ts and other sectors of final demand, respectively. So long as all that is needed is the input purchases of each industry f rom every other industry in the region, as opposed to the total input purchases of each industry, it would seem simpler to design a survey ins t rument which is a imed at filling in the rows as opposed to the columns. Generally, a firm produces a smaller number of outputs than it buys inputs, and it is more likely that they will know to whom they sell in the region than f rom whom they buy. Where it would be necessary to know total inputs including amounts imported, it would, of course, be necessary to fill up the table, column by column, based on either survey data on inputs or production function assumptions. But which kind of inter industry formulat ion seems most appropr ia te is really a methodological question, that is, it depends upon the kinds of questions which we want the accounts sys tem to be able to answer. Tha t is the subject of the next section.

III. SOME MATTERS OF METHODOLOGY

In this section, the discussion will turn to some mat te r s concerning the way in which par t icular i tems in the accounts are to be defined and the way in which certain analytical relationships are to be determined, but all within the context of accounts based on a simple economic base or foreign-trade mult ipl ier theory. Discussion of the viabi l i ty of such a simple theoretical underpinning will be covered in the next section.

Let us turn first to the question of the appropr ia te form in which to express in ter industry relationships. As has been pointed out earlier, the most useful information would be a complete inter industry account, made up of a ma t r ix of total in ter indust ry inputs and a ma t r ix showing the amount of each input obtained as imports. The necessi ty of obtaining imports by supplying industries (as opposed s imply to total imports of each domestic industry) is necessary to allow fully for the effects of the industrial composition of changes in final demand on ac t iv i ty levels. The determinat ion of such an account would require the est imation of two of the following three sets of information: 1) the technologically required total inputs of every domestic industry, 2) the inputs of every domestic industry supplied by other domestic producers, 3) the imports inputs of every domestic industry. Two of the three sets would suffice, since the ma t r ix represented by the first set would be the sum of the other two matrices~ A question which has been raised earlier, and which still seems appropr ia te is, "Which set of information would be most useful if only one set could be obtained? ''~8 Clearly, the import information alone would be of re la t ively litt le use. The choice between the other two would seem to depend largely on a judgment as to the relat ive importance of changes in technology as opposed to changes in t rading relationships (the pro- portion of each input obtained f rom domestic as opposed to foreign sources) as

~s Leven, loc. eit.

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a determinant of changes in act ivi ty levels, given the level of final demand. As-pointed out in earlier work, the choice would seem to depend on the size and complexi ty of the region 's economy. Where t rade is small relat ive to total act ivi ty, say for the United States, the first set of information, that is, an input-output table seems called for. For even a fair ly large metropoli tan region, however, changes in t rading relationships s temming from changes in relat ive prices and f rom local agglomerat ion are likely to dominate technological change and so the second set of information seems called for. For want of a bet ter name this has been called a " f rom- to" table. 89

As indicated in Figure 1 (ignoring the dotted line), the error in projections of act iv i ty levels s t emming f rom changes in t rading relationships is likely to be quite large for a very small area, falling ra ther sharply to a quite small amount for the United States, as a whole. Errors due to changes in technological requirements , however, would be likely to be fair ly invariant with respect to

Forecasting error

from assuming

constant

structure

(per cent)

~ Aisumlng constant ...................................... ~ radmg pattern

/Assuming constant technology

200 POPUL&TION OF REGION

(mLU0NS) FIGURE 1

regional size. Technological change still is l ikely to be fair ly important , even in a very small region. As the figure is drawn, it indicates that " f rom- to" tables would dominate up to a region as large as about half the United States ' population. But note that there are no scales indicated on the vert ical axis. While one can speculate on the relat ive slopes of these lines, it seems much more difficult to speculate even about their relative, much less absolute, ordinates. Accordingly, their relat ive positions easily could be as shown by the dotted line, where " input -output" tables dominate for all except the very smallest regions. Determining the relat ive slopes and positions of such lines still appears to be a worthwhile research task.

Another methodological ma t t e r concerns the definition of the foreign-trade multiplier. In this connection two issues not previously discussed at all will be raised, both relat ing to misconceptions in the present au thor ' s earlier

89 Leven, op. ei~., p. 170.

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work and previously undetected by the author, or, apparent ly , by anyone else. In earlier work the foreign-trade mult ipl ier for a single region vis-a-vis the rest of the world was determined as

1 1 - Vc/Y~ (1)

where Vc is the value added in the region, direct ly and indirectly, in the production of goods for personal consumption, and Yp is the total value added or, approximate ly , the gross product produced in the region. 4~ Where inves tment is regarded as endogenous and Vz is the value added in production of inves tment goods, the mult ipl ier would have been

1 1-- (Vc + V~)/Yp " (2 )

The rat io of Vc/YP is s imply an average approximat ion to the marginal propensi ty to generate value added domestical ly in the production of goods for consumption; it is the value added equivalent of the marginal propensi ty to consume domestical ly produced goods, which, in turn, is nothing more than the difference between the marginal propensi ty to consume and the marginal propensi ty to import .

The mult ipl ier formulat ion indicated above is seriously in error in two respects. First , it makes no allowance for differences in the size of the multiplier, depending on the industrial composition of a change in some category of final demand, say export demand. I t was the possibil i ty of allowing for just such differences which served as much of the rat ionale for incorporat ing in ter indust ry calculations into the accounts in the first place. Second, the marginal propensi ty to consume is re lated not to the increment to regional disposable personal income, but to regional gross product! This destroys most of the point of even bothering to determine Ya in the accounts. Accordingly, the mult ipl ier formula should be

1 zlVx(I-- T)-I/,JVx 1-- Vc YR (3 )

YR YP

where Vc, Yp and YR are all scalar quantit ies, as defined earlier, z/Vx is a (1 • n) vector, indicating the change in value added by industry resul t ing direct ly f rom a specified change in the export bill of goods, 41 and ( I - - T) is an (n • n) mat r ix , where T is the ma t r ix of from-to coefficients. Both for con- venience and for other reasons to be discussed below, the formula is wr i t ten

40 For derivation of the formula see Leven, loc. cir., p. 236, and for the reconciliation between the definitions of value added and gross product see Leven, op. cir., footnote 17.

41 The symbol V~ did not appear in earlier versions of the author's work. It is not to be confused, however, with Ve the value added directly and indirectly in production for export. V~ is direct value added only. Its symbolic equivalent in Leven, op. cir., would be

v~; (i : 1 . . . . . n) �9


in terms of average rather than marginal relationships, but it will be simpler for the moment to discuss them as if they were written in marginal terms.

In any event, the product of the first two scalar terms represents the foreign-trade multiplier for a change in export demand which generated no further interindustry effect at all. The term Vc/Y~ is the domestic value added, directly and indirectly, out of the propensity to consume out of domestic disposable personal income. There is no necessity to calculate value added indirectly in production for consumption on an interindustry basis as long as we assume unit income elasticity of consumption demand for all commodities. If this were not the case and some other consumption bill of goods were

specified, the scalar quantity Vc would be replaced by the scalar ~ V~ ( I - T) -1. i = l

Note that while Vc is a scalar quantity indicating the total value added in consumption in all industry's products, V~ is a vector showing value added in the production of goods for consumption industry by industry. This vector multiplied by the matrix ( I - - T ) -1 and summed over i industries results in a scalar quantity.

The second term is simply the propensity to generate personal disposable income to the region's residents out of an increase in gross product produced in the region. Thus, generalizing with respect to consumption, but continuing to treat investment as exogenous, the foreign-trade multiplier would be

1 �9 AVx( I - - T) - I /AVx. Y. v o ( I - T) -~ YR / ( 4 )

1 Y~ YP

This is the regional accounts equivalent to the nonbasic:basic employment multiplier concept.

The third term in equation (3) is the vector by industry of the change in value added directly and indirectly from production to export resulting from a given change in value added directly in producing for export (Vx alone is the direct value added). To express this in terms of the effect of a change in export sales on value added or employment, substitute ASx. Vx/Sx for AVx, where ASx is the vector of changes in export sales by industry. Then the foreign-trade multiplier with respect to the effect of change in sales on total value added or employment would be

1 �9 ASx Vx 1/ASx ~. V,(I -- T) -~ Y~ " ~ x (I -- T)- .

i__ ~ __ / (5) YR YP

These multipliers naturally would be smaller than the employment or value- added multipliers due to trade leakages from the import of raw materials for the production of exports. In other words, the impact of an extra dollar of export sales obviously would be less than of an extra dollar's worth of value added in producing for export.

As seen in Table 1, the reformulation of the multiplier does make a differ-

LEVEN: REGIONAL AND INTERREGIONAL ACCOUNTS IN PERSPECTIVE ] 3 9

TABLE 1 FOREIGN-TRADE EMPLOYMENT OR VALUE-ADDED MULTIPLIERS,

BY INDUSTRY OF CHANGE IN FINAL DEMAND, SIOUX CITY, 1958"

Household Interindustry Industry • Component = Component Multiplier

Agriculture Meat Packing Other Food Processing Other Manufacturing Transportation and

Communication Trade Finance, Insurance,

and Real Estate Services

1.55 1.55 1.55 1.55

1.55

1.55

1.55

1.55

1.04 1.21 1.10 1.11

1.06

1.30

1.10

1.13

1.62 1.87 1.71 1.72

1.64

2.01

1.70

1.74

* Computed from data in "Sioux City Economic Report, 1959." Note: These show the multiplier effect of a unit change in export employment or

value added. The effect of a unit change in export sales on export employment or value added would be smaller.

ence in the quantitative results, at least for certain industries, and at least in Sioux City, where revised figures could be derived. The value computed on the basis of equation (1) was 1.64. So far as the household multiplier is concerned, the difference is limited in that where YR is less (greater) than Yp, the first term of equation (3) will be bigger (smaller), but the second term will be smaller (bigger) as compared will the earlier formula, equation (1).

Another problem in deriving multiplier values is deciding whether average or marginal propensities should be used. As a practical matter where data have been collected only for a single time period and no cross-section data are available, the average relationships are all that can be computed anyway. Even so, a rationale for actually preferring average-to-marginal relationships has been constructed. 42 The essence of the argument is that where growth in regional income takes the form of an increase in the number of employed persons, with average income per worker remaining the same, the region's marginal propensity to consume is actually the average propensity to consume of future residents, who probably can be assumed to have pret ty much the same spending habits as the present residents. Implicit in the argument is that where increased income takes the form of increased average income to a fixed labor force, the appropriate measure of the region's marginal propensity to consume is the marginal propensity to consume of these workers. But marginal propensity to consume over what period? For the United States as a whole, the average propensity to consume has remained quite stable over several decades. This suggests a good possibility that in the context of analyzing long-run regional growth, the average

42 Tiebout, op cir.


propensity to consume might be the appropriate measure, both for determining the impact of increased number of workers and increased earnings per worker even if a measure of the short-run marginal propensity to consume were available.

Taking YR/Yp as an approximation for dYR/dYp may be a more serious matter. This assumes a constant proportionality between labor commutation rates, net receipt of property income from abroad, taxes net of transfer payments to nonlocal government, and undistributed profits of domestic corporations, all with respect to gross product originating in the region. In most cases, it would seem prudent, at least, to consider making adjustments for these assumptions, but it is hard to see how they could be made in other than an ad hoc manner.

A final methodological point concerns the explicit definition of direct exports. In regional accounts, as in the national accounts, the definition has been extended to include "invisibles," including, in addition to services, commodities purchased by nonresidents while in the region. But, to some extent, this begs the question of who is a resident. In particular, it requires some decision with respect to the residence classification of institutional populations, such as stu- dents, mili tary personnel, and inmates of prisons and state hospitals. In general, such individuals have been regarded as members of the local community, 4~ and their personal outlays regarded as local consumption. 44 While the people involved are transients, they are likely to be replaced by other transients, much like themselves. While satisfactory, this t reatment is arbitrary and opens up the whole question of regional definition in a functional context. Some of the major alternatives which seem to exist are to define the region as all of the people working there, or living there, or perhaps buying there. ~5 This, however, is more a conceptual than a methodological issue and it will be discussed in the next section.

IV. SOME CONCEPTUAL ISSUES

This concluding section primarily will at tempt to re-evaluate the concept of "export or die," inherited from economic base theory and still the funda- mental theoretical underpinning of most work in regional accounts. Let me state r ight at the outset that I think that this concept may be seriously inadequate. While not a convincing counter-argument, it is still somewhat disturbing to note that the economy of the world as a whole does grow without exporting anything (the sending of missiles into space would be a unilateral transfer; not an export).

For metropolitan regions it is probably true that increasing size, almost invariably, is associated with an increasing absolute level of income earned

4s Although their support typically would be accounted for as a transfer from abroad. ~4 Outlays on local goods of the institutions with which they were associated might,

however, be classed as exports if these were instrumentalities of nonlocal government. 45 For a discussion of the problems of assymetry between alternative definitions see

W. Hochwald, "Conceptual Issues of Regional Income Estimation," in National Bureau of Economic Research, Studies in Igzcome and Wealtl*, XXI.

LEVEN: REGIONAL AND INTERREGIONAL ACCOUNTS IN PERSPECTIVE ] 4 1

through exporting/6 But this is hardly a convincing demonstration of a causal relationship. For example, it is also true that a rising level of aggregate income in any economy would virtually always be associated with a rising absolute level of net investment. But even though this is the case, most of us regard businessmen's statements to the effect that the only way to secure economic growth in the American economy is by creating inducements for private business investment as at best misguided, and at worst dangerous half-truths.

At the same time, however, we do not always see the same kind of limited applicability in the export theory of regional growth determination. We have probably paid too little attention to Professor Tiebout 's uneasiness on this score several years ago. 47 At that time the answer to the queston "Can a region grow without an increase in exports?" intuitively seemed to be "Yes ." Unfortunately, this observation was waylaid by the observation that increased regional size was associated with increased export volume. In re- considering that controversy at this time, it seems appropriate to consider the possibility that, at least in part, increased exports may be a consequence, not a cause of increased growth in increased per capita real income.

To illustrate, suppose we have a three-person economy on a remote island, consisting of two barbers and a masseur, who provide each other with personal services, otherwise living on wild nuts and berries. Under such conditions, increased productivity in their pr imary occupations would lead to increased real income. This greater productivity initially might take the form of increased leisure for all of them. But it also might result in a sufficient increase in the haircut price of musical entertainment, the haircut price of massages remaining the same, to induce one of the barbers to forsake his shears for a fiddle. Or, in the absence of a lack of musical ability on the part of any of the aboriginal inhabitants, they might bid up the price of musical entertainment sufficiently high to persuade a musician to immigrate to their island. Quite clearly growth in per capita income could proceed indefinitely without external trade limited only by the productivity of the inhabitants of the island and the possible gains from the division of labor. Accompanying growth in the island's population could also increase indefinitely without external trade, limited only by the foregoing limitations and by a continued differential of per capita real income of the islanders over levels someplace else, including full allowance for detractions to real income stemming from congestion. ~8

46 The relationships of size to gross export sales would probably not be so regular due to wide variations in the imported raw material component of different commodities in different places.

47 See Tiebout's exchange with North some years ago. The real limitation of that discussion was that the only real alternative explanatory variables considered explicitly were autonomous investment or shifts in the consumption function; in short, traditional Keynesian variables, which are most applicable only to problems of change in the short run. See Tiebout, "Exports and Regional Economic Growth," North, "A Reply," and Tiebout, "Rejoinder," JournM of Political Economy, April, 1956.

4s Moreover, in a more realistic situation where we assumed some small but not in- creasable amount of initial trade throughout, the process could be accelerated by induced agglomeration of industries to supply input needs of domestic producers; in this case, exports might actually decrease!

1 42 PAPERS OF THE REGIONAL SCIENCE ASSOCIATION

But there is something else that is also likely to happen to the island's economy. Specifically, opportunities for the division of labor are not likely to be exhausted within the island. Comparative advantages in production most probably would arise and trade with other regions would occur. Moreover, so long as the possibility of gains from trade is not exhausted, the absolute volume of t~ade would increase along with the increase in the island's total population.

Basically, then, in this example the driving force behind economic growth is rising productivity. This is hardly a very startl ing statement. Such increased productivity could stem from increases in the stock of physical capital, but also from increases in the stock of human capital, from resource discovery, from invention, or from a change in tastes. The increase in the volume of trade is simply an expected consequence of market adjustments to higher productivity. It is generated mainly by the proliferation rather than intensification of human wants as real income rises and by secular changes in technology which tend to increase the technological possibilities for exploiting the division of labor. 49

What the foregoing discussion seems to indicate is the desirability of recon- sidering both the delineation of sectors of final demand and the definitional distinction between final and intermediate production. This latter distinction as well as the sector definitions is arbitrary. For example, "Is the cost of air-condition- ing an office an intermediate business input or wages in kind to the employees?"

As noted above, almost all work in regional accounts has proceeded on the basis of a consumption-investment-government-rest of the world sectoring, or some simple variant thereof. In t rying to develop a new theoretical conception of regional growth, it might be useful to reconsider the appropriateness of this particular sectoring.

Turning first to exports, the relevant question is whether they really are independent of activity levels within the region. Here it might be useful to distinguish between exports of commodities for which per capita demand is a decreasing function of distance, and those for which it is not. The former group would probably be most trade and personal services and some business services. The reason for this distinction, of course, is that exports of the first type are likely to generate feedback effects, while the latter would not. For example, increased exports to the surrounding hinterland would increase income in the region, which would increase imports from the hinterland, which would increase its income and imports, and hence further increase exports of the region. Even where there might be large trade to the hinterland, however, it would not necessarily be important to segregate it into a separate sector unless the region were also significant in the hinterland's export market. 5~

~9 I am indebted to my former colleague, Professor Nathan Rosenberg, now of Purdue University, for reacquainting me with the fact that Adam Smith did have something useful to say about economic development.

50 This discussion of the export sector really opens up anew the whole question of geographic delimitation of regions. For the most part, metropolitan regions have been defined so as to approximate a closed labor market. A closed retail shopping market also could be used as a definition. In this case, though, we would have to be prepared to find more overlapping of adjacent areas than in the case of labor market areas. In any event, this is outside the scope of this paper.

LEVEN. REGIONAL AND INTERREGIONAL ACCOUNTS IN PERSPECTIVE ] 43

So far as investment is concerned, some revisions also seem to be in order. In the case of residential investment , it would seem to be just as closely related to consumer income as any other category of consumer spending in the long run. Therefore , it might be useful to redefine inves tment so as to exclude residential construction. In the long run, inves tment in inventories ought to be very closely related to output levels; hence, they probably could be regarded as in termediate inputs. The re would be a stat ist ical problem here, however, in tha t data for a single year could not necessari ly be regarded as reflecting equil ibrium inventory-sales ratios.

Th is would leave only business plant and equipment expenditures left in investment . These could be broken down usefully in two ways. First , plant could be distinguished f rom equipment; square feet of floor space may va ry more direct ly wi th output than the amount of equipment. This is, of course, a s ta tement which does require verification. Second, so far as increases in inves tment are concerned, it might be useful to separate them into increased inves tment expected in es tabl ishments a lready exist ing in the region f rom inves tment in establ ishments to be s tar ted anew. And the la t ter might be broken down into those expected to go into exis t ing s t ructures and those expected to go into new structures.

Government presents more of a problem. 51 Outlays, both current and capital, of local government which are of the type that are primarily locally financed might go back into the in ter industry matr ix; the hypothesis is tha t they are close to unit communi ty- income elastic in the long run. Local expenditures of the type ordinari ly financed mainly by grants and aids f rom state or federal government would remain as a separate sector of final demand, with current and capital outlays probably separated.

Sales to agencies of s tate and federal government total ly outside the region can probably be regarded as a single exogenous category of final demand. The only likely problem tha t might arise would be the necessi ty of allowing for " feedbacks . " In this regard, however, expor ts to government would be no different in principle than exports to pr ivate purchasers. Feedbacks might be especially important for a metropoli tan area which const i tuted a large share of a s ta te ' s , or maybe even the nation's , tax base.

This still leaves sales to agencies of nonlocal government which are located within the region itself. This is probably the most difficult, though cer ta inly not the most critical, par t of the government sector to account for. Some sales, like those to a local air base, clearly are exports , and wi th no more chance of manifest ing a feedback relat ionship than if they were far away. On the other hand, things like postal services, mea t inspection, and many judicial functions could be regarded as local activities, ei ther for inter industry uses or final consumption, and could be so accounted for. The cost of providing them would be accounted for as a t ransfer payment in kind to the region 's residents or firms using the services. Also, in this case it might seem well to separate

51 In much of the author's earlier work, the government sector was suppressed into the other sectors, but this was mainly for reasons of expedience or simplicity. It was never argued that these were generally defensible grounds for such treatment.


current f rom capital outlays, if possible. So far as consumption is concerned, there would seem to be some sense

in t ry ing to separate it into three categories, consumption of goods with known and fairly constant population elasticities of demand, consumption of goods wi th known and fair ly constant income elasticities of demand, and other consumption. The first two categories could be fit into the in ter industry mat r ix and the last left as a sector of final demand. This and other suggestions made for redefining the sectors of final demand involve put t ing some par ts of final demand into the inter industry matr ix . There mus t also be a consideration of whether anything in the inter industry ma t r ix should be brought out into the final demand sector.

In this regard it should be noted that this is not meant as an a t t empt to ma im or disfigure inter industry or income and product accounts, but ra ther an a t t empt to use them more effectively as techniques for s t ructural analysis. I t mus t be recognized that accounts aimed at explaining changes in act ivi ty levels should not necessarily be designed in the same way as those geared to measure aggregate income in a welfare context or act ivi ty levels in the context of nonviolation of factor input constraints. With this in mind, it would seem advisable to take a much closer look at the distinctions we have made between intermediate and final output. I t seems a little foolish, for example, to t reat household expenditures on toothpaste as exogenous and business outlays on research and development as endogenous, even in the short, much less the long run. The whole business-services area, including mainly outlays for adminis- t ra t ive and auxil iary activities, would appear to include many likely candidates for t ransfer f rom the inter industry ma t r ix to final demand.

Obviously, all of these remarks about resectoring are intended nei ther as firm recommendat ions nor expressive of an explicit theoretical reformulat ion, al though they do reflect hypotheses about the nature of regional growth. Rather, they are meant mainly as a plea for a more flexible use of social accounts. We should be very careful to r emember tha t there is no logically correct way of set t ing up regional, or any other accounts, for that mat te r , independently of a preconceived analytical purpose to which they are to be put. In fact, it was the absence of such a preconceived analytical purpose that gave Professor Andrews so much difficulty in deciding what was the r ight unit of account for economic base studies. As a consequence, we should not expect that a part icular set of definitions necessarily will hold for different questions, or even for the same questions in different kinds of regions or at different stages of a given region 's development.

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Regional and interregional accounts in perspective